PRESSURE-TEMPERATURE-REACTION AFFINITY MAPS AS A MEANS TO PREDICT METAMORPHIC REACTION OVERSTEPPING

Metamorphic reactions may be overstepped in temperature due to kinetic barriers to nucleation and growth. The extent to which these kinetic barriers delay the onset of reaction is related to the reaction affinity of each reaction, defined herein as the Gibbs free energy difference between the thermodynamically stable, but not-yet-crystallized, products and the metastable reactants. For oversteps in temperature (DT), reaction affinity is, in turn, related to the entropy difference (DS) between these two states through the relation A = DT * DS. Calculating reaction affinity in natural systems is difficult because compositional departures of reactant and product phases from equilibrium cannot be predicted: some reactant phases may change composition as the reaction is overstepped whereas others may not, and the composition of product minerals that do finally nucleate and grow are unknown other than within limits. This has led several authors to estimate reaction entropy and reaction affinity using simplified end member reactions that provide an approximation to the more complex reactions that actually proceeded in the rocks. A deficiency in this approach is the changing compositions of solid solution phases in multivariant reactions. We report here some attempts to calculate reaction affinity in more complex (realistic?) chemical systems, using Theriak-Domino. The most promising to date involves excluding the product phase of interest (e.g., garnet) from the rest of the mineral assemblage (e.g., muscovite+chlorite+biotite+quartz+plagioclase), but monitoring it’s Gibbs free energy with respect to the rest of the mineral assemblage. For a given amount of overstepping in temperature of the thermodynamically-predicted garnet-in reaction, the free energy difference between the two gives a direct measure of the reaction affinity. Pressure-temperature-reaction affinity ‘maps’, in concert with P-T phase diagram sections, illustrate expected differences in reaction affinity as a function of overstepping in different domains of a phase diagram (e.g., low variance vs high variance domains), and therefore may prove to be useful tools for predicting in what domains of a phase diagram kinetic barriers to nucleation and growth result in overstepped or discontinuous reaction, rather than continuous reaction as predicted by equilibrium modeling.